The quote is out of context: In case of infinite reserve (and infinite time to place your bets ;)), there are no catastrophic losses which would stop you from betting again.
The problem with always doubling your wager is that the exponential growth will eventually reach any finite limit in case of a run of 'bad luck'. Without limit, that's not an issue and you'll only lose when you never win any bet, which 'almost surely' won't happen.
The problem with always doubling your wager is that the exponential growth will eventually reach any finite limit in case of a run of 'bad luck'. Without limit, that's not an issue and you'll only lose when you never win any bet, which 'almost surely' won't happen.